Lesson 1: Whole Number Operations

Property

Each place represents 10 times the place just to the right. A number is a sequence of digits, and its value is the sum of each digit multiplied by its place value (a power of ten). For example:

This can also be written using exponents:

Examples

• The number 5,281 in expanded form is $5 \times 1000 + 2 \times 100 + 8 \times 10 + 1$.
• The number 709 shows the importance of zero as a placeholder. It is $7 \times 100 + 0 \times 10 + 9$.
• A larger number like 4,600 is written as $4 \times 1000 + 6 \times 100 + 0 \times 10 + 0 \times 1$.

Explanation

Place value is like a secret code where a digit's position tells you its real worth. A 7 in the tens place is 70, but in the hundreds place, it's 700! This system lets us write any number, big or small.

Property

Each operation has specific key words that signal which calculation to perform:

• Addition ($+$): sum, total, altogether, combined, increased by, more than
• Subtraction ($-$): difference, less than, decreased by, fewer, take away, remaining
• Multiplication ($\times$): product, times, of, groups of, repeated addition
• Division ($\div$): quotient, divided by, shared equally, groups, per, average

Examples

Property

When adding multi-digit whole numbers, align digits by place value: ones under ones, tens under tens, hundreds under hundreds, etc.
The sum is calculated column by column from right to left, carrying over when a column sum exceeds 9.

Examples